Okay, we are tasked with adding 8966 and 8631. Let's begin!

Step 1: We'll start by adding the digits 6 & 1 in column 1 and get 7.

Step 2: We'll start by adding the digits 6 & 3 in column 2 and get 9.

Step 3: We'll start by adding the digits 9 & 6 in column 3 and get 15.
We'll write down the last digit 5 and carry the 1 to the next column.

Step 4: We'll start by adding the digits 8 & 8 in column 4 and get 17.
We'll write down the last digit 7 and carry the 1 to the next column.

So, 8966 + 8631 = 17597.

